THE FLT PROCEEDED WITHOUT INCIDENT UNTIL THE PLT CONTACTED HOUSTON ARTCC. THE PLT REQUESTED THE DESTINATION WX & WAS TOLD THAT THE ENTIRE AREA WAS IFR. THE CLOSEST ARPT REPORTING VFR CONDITIONS WAS AT MCALLEN, TX, APRX 80 MI SOUTHEAST. THE PLT THEN ADVISED THAT HE DID NOT HAVE ENOUGH FUEL TO REACH MCALLEN. AT 1828 CST, HE ADVISED THAT THE DESTINATION ARPT WAS SIGHTED BELOW. THE CONTROLLER ACKNOWLEDGED & CLEARED THE PLT TO CHANGE FREQUENCY FOR LANDING. ABOUT 7 MIN LATER, THE ACFT CRASHED IN OPEN MESQUITE RANGE WHILE IN A SLIGHT NOSE DOWN, SLIGHT LEFT BANK ATTITUDE, AT HI SPEED. RADAR DATA SHOWED THAT AFTER THE PLT'S LAST RADIO TRANSMISSION, THE ACFT OVERFLEW THE ARPT, TURNED LEFT & PROCEEDED NORTH, AWAY FROM THE ARPT, ABOUT 5 MI NORTH, IT MADE A 360 TURN, THEN CONTINUED 2 TO 3 MI FURTHER NORTH. A 180DEG TURN WAS THEN MADE & RADAR CONTACT WAS LOST. DURING THAT TIME, THE ALT VARIED CONSIDERABLY. A RANCH FOREMAN HEARD THE ACFT FLYING AROUND BEFORE IT CRASHED. HE REPORTED AN OVERCAST WITH FOG & VISIBILITY LESS THAN 1/8 MI.